This sounds like it could be pretty spicy, allspice is pretty potent. Also, I don't see the brown sugar being necessary, I would increase the honey to at least 2 lbs per gallon for sweeter mead. If you use pasteurized apple juice, heating the juice and honey is not necessary. Put a gallon or two of juice in the carboy with the honey, and shake like mad to mix and aerate. add the spices (half what is there) and top up with more juice. Add yeast. Make sure you leave plenty of head space, this will foam up as it ferments. Primary fermentation will probably take several weeks to a month, maybe longer, depending on temperature. Try to keep it 62-68 degrees. When the airlock slows down and the gravity is stable over a week, rack it to secondary, and taste it. Add more honey if you think it is not sweet enough. It will need to sit in secondary for a few months till clear.

Don't heat anything. Put one gallon of juice in your carboy, add half the honey, shake like h*ll. Put juice into the honey container, cover and shake, shake, shake. Add this to the carboy, and repeat until all the honey is dissolved. Toss int the spices. Shake some more. Pitch the yeast, plug with bung and fermentation valve. It will foam up when fermentation starts. After fermentation slows, rack to a second fermentor, and leave till clear. Overall, it will take a few months.

I would increase the honey to a least five pounds. Use pastuerized unfiltered apple juice if you can find it. It will add complexity to final product. Cut the spices in spices such as cinnamon, allspice etc. Alcohol will intensify these flavors ,this will add to the aging time.
Rick.
Primaries Nothing waiting for Apple juice to appear.
Secondary 1: Peach spice mead
Secondary 2: Peach Aprocit Mead
Secondary 3: Vanilla Mead
In Bottles Traditional Mead (just finished bottling) Cyser(down to last two bottles), Cranberry-Orange, Plum Meads